結果
| 問題 |
No.3045 反復重み付き累積和
|
| コンテスト | |
| ユーザー |
 naniwazu
|
| 提出日時 | 2025-02-04 04:16:57 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 3,924 ms / 5,000 ms |
| コード長 | 7,158 bytes |
| コンパイル時間 | 727 ms |
| コンパイル使用メモリ | 81,920 KB |
| 実行使用メモリ | 91,140 KB |
| 最終ジャッジ日時 | 2025-02-04 04:17:43 |
| 合計ジャッジ時間 | 43,300 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 41 |
ソースコード
_fft_mod = 998244353
_fft_imag = 911660635
_fft_iimag = 86583718
_fft_rate2 = (
911660635,
509520358,
369330050,
332049552,
983190778,
123842337,
238493703,
975955924,
603855026,
856644456,
131300601,
842657263,
730768835,
942482514,
806263778,
151565301,
510815449,
503497456,
743006876,
741047443,
56250497,
867605899,
)
_fft_irate2 = (
86583718,
372528824,
373294451,
645684063,
112220581,
692852209,
155456985,
797128860,
90816748,
860285882,
927414960,
354738543,
109331171,
293255632,
535113200,
308540755,
121186627,
608385704,
438932459,
359477183,
824071951,
103369235,
)
_fft_rate3 = (
372528824,
337190230,
454590761,
816400692,
578227951,
180142363,
83780245,
6597683,
70046822,
623238099,
183021267,
402682409,
631680428,
344509872,
689220186,
365017329,
774342554,
729444058,
102986190,
128751033,
395565204,
)
_fft_irate3 = (
509520358,
929031873,
170256584,
839780419,
282974284,
395914482,
444904435,
72135471,
638914820,
66769500,
771127074,
985925487,
262319669,
262341272,
625870173,
768022760,
859816005,
914661783,
430819711,
272774365,
530924681,
)
def _butterfly(a):
n = len(a)
h = (n - 1).bit_length()
len_ = 0
while len_ < h:
if h - len_ == 1:
p = 1 << (h - len_ - 1)
rot = 1
for s in range(1 << len_):
offset = s << (h - len_)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p] * rot % _fft_mod
a[i + offset] = (l + r) % _fft_mod
a[i + offset + p] = (l - r) % _fft_mod
if s + 1 != (1 << len_):
rot *= _fft_rate2[(~s & -~s).bit_length() - 1]
rot %= _fft_mod
len_ += 1
else:
p = 1 << (h - len_ - 2)
rot = 1
for s in range(1 << len_):
rot2 = rot * rot % _fft_mod
rot3 = rot2 * rot % _fft_mod
offset = s << (h - len_)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p] * rot
a2 = a[i + offset + p * 2] * rot2
a3 = a[i + offset + p * 3] * rot3
a1na3imag = (a1 - a3) % _fft_mod * _fft_imag
a[i + offset] = (a0 + a2 + a1 + a3) % _fft_mod
a[i + offset + p] = (a0 + a2 - a1 - a3) % _fft_mod
a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % _fft_mod
a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % _fft_mod
if s + 1 != (1 << len_):
rot *= _fft_rate3[(~s & -~s).bit_length() - 1]
rot %= _fft_mod
len_ += 2
def _butterfly_inv(a):
n = len(a)
h = (n - 1).bit_length()
len_ = h
while len_:
if len_ == 1:
p = 1 << (h - len_)
irot = 1
for s in range(1 << (len_ - 1)):
offset = s << (h - len_ + 1)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p]
a[i + offset] = (l + r) % _fft_mod
a[i + offset + p] = (l - r) * irot % _fft_mod
if s + 1 != (1 << (len_ - 1)):
irot *= _fft_irate2[(~s & -~s).bit_length() - 1]
irot %= _fft_mod
len_ -= 1
else:
p = 1 << (h - len_)
irot = 1
for s in range(1 << (len_ - 2)):
irot2 = irot * irot % _fft_mod
irot3 = irot2 * irot % _fft_mod
offset = s << (h - len_ + 2)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p]
a2 = a[i + offset + p * 2]
a3 = a[i + offset + p * 3]
a2na3iimag = (a2 - a3) * _fft_iimag % _fft_mod
a[i + offset] = (a0 + a1 + a2 + a3) % _fft_mod
a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % _fft_mod
a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % _fft_mod
a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % _fft_mod
if s + 1 != (1 << (len_ - 1)):
irot *= _fft_irate3[(~s & -~s).bit_length() - 1]
irot %= _fft_mod
len_ -= 2
def _convolution_naive(a, b):
n = len(a)
m = len(b)
ans = [0] * (n + m - 1)
if n < m:
for j in range(m):
for i in range(n):
ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
else:
for i in range(n):
for j in range(m):
ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
return ans
def _convolution_fft(a, b):
a = a.copy()
b = b.copy()
n = len(a)
m = len(b)
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
_butterfly(a)
b += [0] * (z - m)
_butterfly(b)
for i in range(z):
a[i] = a[i] * b[i] % _fft_mod
_butterfly_inv(a)
a = a[: n + m - 1]
iz = pow(z, _fft_mod - 2, _fft_mod)
for i in range(n + m - 1):
a[i] = a[i] * iz % _fft_mod
return a
def _convolution_square(a):
a = a.copy()
n = len(a)
z = 1 << (2 * n - 2).bit_length()
a += [0] * (z - n)
_butterfly(a)
for i in range(z):
a[i] = a[i] * a[i] % _fft_mod
_butterfly_inv(a)
a = a[: 2 * n - 1]
iz = pow(z, _fft_mod - 2, _fft_mod)
for i in range(2 * n - 1):
a[i] = a[i] * iz % _fft_mod
return a
def convolution(a, b):
"""It calculates (+, x) convolution in mod 998244353.
Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1],
it calculates the array c of length n + m - 1, defined by
> c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353.
It returns an empty list if at least one of a and b are empty.
Constraints
-----------
> len(a) + len(b) <= 8388609
Complexity
----------
> O(n log n), where n = len(a) + len(b).
"""
n = len(a)
m = len(b)
if n == 0 or m == 0:
return []
if min(n, m) <= 0:
return _convolution_naive(a, b)
if a is b:
return _convolution_square(a)
return _convolution_fft(a, b)
N, Q = map(int, input().split())
A = list(map(int, input().split()))
for _ in range(Q):
query = list(map(int, input().split()))
if query[0] == 1:
k, x = query[1:]
weight = [1] * N
for i in range(N - 1):
weight[i + 1] = (
weight[i] * k * (x + i) * pow(i + 1, -1, _fft_mod) % _fft_mod
)
A = convolution(A, weight)[:N]
else:
x = query[1]
print(A[x - 1])